Soft Hair as a Soft Wig

TL;DR

The paper analyzes large gauge transformations in 4D asymptotically flat spacetimes, showing that soft (infrared) degrees of freedom can be cleanly decoupled from hard scattering through a canonical (and, quantum mechanically, unitary) dressing.By constructing explicit factorization both at the classical and quantum levels for U(1) and BMS symmetries, the authors demonstrate that soft hair evolves trivially and does not constrain hard scattering, undermining claims that asymptotic symmetries resolve the black hole information paradox.The work provides a physical interpretation of the dressing as removing the long-range field contribution, yielding a soft-free description of scattering, and extends the factorization to gravitational memory observables, which can be dressed to be soft-independent.Overall, the results connect infrared structure, memory effects, and asymptotic symmetries into a consistent framework where soft hair constitutes a wig rather than a source of observable information in scattering.

Abstract

We consider large gauge transformations of gravity and electromagnetism in D=4 asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large U(1) charge conservation. Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region; they scatter trivially in their own sector. This implies in particular that the large gauge symmetries bear no relevance to the black hole information paradox. We also present the quantum version of soft decoupling. As a consistency check, we show that the apparent mixing of soft and hard modes in the original variables arises entirely from the long range field of the hard charges, which is fixed by gauge invariance and so contains no additional information.